# Understanding Lucky Dough Chances

• The Lucky Dough game consists of a square with nine boxes.
• The player selects a number from 1 to 5 in each of the eight boxes; the center box is always a free match.
• The more lines a player matches, the bigger the prize.

### You Can Calculate the Odds of Winning Lucky Dough.

To calculate the odds of winning the game, here are a few terms you'll need to know:

F = Field Size, or the number of numbers that can be drawn in any box. In this case, it is always 5.
N = Number of Fields
, or the number of boxes in the game. It's always 8 in this game, since the center box is
always a free match.
M = Number of Fields Not Matched, or missed fields.
P = Number of Permutations, or possible outcomes that can result from a drawing.
C = Combinations that form a line.

^ = Symbol representing an exponential; directs us to raise that number to the nth power.
For example, 3^ means 3 x 3 x 3, or 3 to the 3rd power.
* = Symbol representing multiplication.
For example, 3*3 means 3 multiplied by 3.
/ = Symbol representing division.

### So, let's get started.

The basic formula for calculating the odds of winning in a combinatorial line game looks like this:

 (((F-1)^M)*P) / (F^N)

For any prize level, say three lines, there are numerous combinations of outcomes that can form a line. For example, 14 ways to match in 6 of 8 boxes and form 3 winning lines and 16 ways to match 5 of 8 boxes and form 3 winning lines. When there are numerous combinations possible, they are added together in the numerator of the probability formula.

### Let's work through an example.

It may look hard, but it really isn't. We can find the odds of winning 3 lines by plugging the numbers into the formula above. It looks like this:

(((5-1)^2)*14+((5-1)^3)*16) / (5^8)

((4^2*14)+(4^3*16)) / 5*8
(4 squared times 14 plus 4 cubed times 16 divided by 5 to the eighth power)

((16 times 14) plus (64 times 16)) divided by 390,625

224 plus 1024 divided by 390,625

1248 divided by 390,625

=0.003195

The odds of winning are 1/.003195

or 313 to 1

You can calculate the odds for other outcomes using this example as your guide.

For any questions regarding the above information, please feel free to contact our Research & Development Division.